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Question

A manufacturing plant has created the following forecast and would like to apply a graphical aggregate planning method. Complete the table and calculate the difference between Jan.'s forecast demand per working day vs a level production model for the entire period?


Month Expected Demand Production Days Demand per Day (to the nearest whole unit)
Jan. 1800 22
Feb. 1400 18
Mar. 1600 21

Answer:


Month Expected Demand Production Days Demand per Day (to the nearest whole unit)
Jan. 1800 22 82
Feb. 1400 18 78
Mar. 1600 21 76

Total expected demand/ Total # working days = level production rate = 79 units/day

Thus the difference between Jan. and the level production is 3 units.

*Note- this problem requires use of basic calculus and have content related to, but not expressly performed in, the text. As such they are more difficult than usual problems and require reflective thinking on the students' behalf.

18) A hotel chain is considering using yield management to increase profits. Its plan is to sell unsold rooms at a discounted rate very close to the night of stay. For example, an unsold Friday night room would be discounted early in the week. It estimates that the percentage of sold rooms (total) would be equal to 50+X, where X is the % discounted off of regular price. Meanwhile the % of rooms sold for full price compared to the discount would be 100-2X (some people would wait to book gambling a discount would happen). Find the ideal discount %.

Answer: Revenue is equal to demand * (% sold at full price * full price +% sold at discounted price * discounted price)

Since no price is given, full price can be assumed to be 100 hundred dollars for calculations, making the discounted price simply 100-X.

Thus revenue is (50+X)[ (100-2x)(100)+(2x)(100-x) ] which simplifies to

-2x^3-100x^2+10000x+500000

Answer

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